分形和科尔恰克定律:历史和修正

IF 0.8 4区物理与天体物理 Q2 HISTORY & PHILOSOPHY OF SCIENCE The European Physical Journal H Pub Date : 2016-02-26 DOI:10.1140/epjh/e2016-60039-8

Attila R. Imre, Josef Novotný

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引用次数: 18

摘要

科尔察克定律——1938年首次以经验形式提出，用来描述各种地理物体(包括湖泊和岛屿)的大小分布。ák -是Benoit Mandelbrot用来证明分形不仅是数学上的怪物，而且它们也适用于描述许多自然物体和现象的例子之一。在本文中，我们将简要概述科尔恰克定律的历史及其与其他类似规则的联系。此外，我们想表明，尽管分形相关定律与korcak定律有相似之处，但korcak指数与分形维数并不直接相关。从这个意义上说，Benoit Mandelbrot基于Kor?ák的实证发现不是分形度量。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Fractals and the Korcak-law: a history and a correction

The Korcak-law – first presented in an empirical form in 1938 to describe the size-distribution of various geographical objects, including lakes and islands by Jaromír Kor?ák – was one of the examples used by Benoit Mandelbrot to show that fractals are not only mathematical monsters, but that they are applicable to describe many natural objects and phenomena too. In this paper, we would like to give a brief overview about the history of the Korcak-law and its connection to other similar rules. Moreover, we would like to show, that although there are similarities between fractal-related laws and the Korcak-law, the Korcak-exponent is not directly related to fractal dimension. In this sense, the measure introduced by Benoit Mandelbrot based on Kor?ák’s empirical findings is not a fractal measure.

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来源期刊

The European Physical Journal H HISTORY & PHILOSOPHY OF SCIENCE-PHYSICS, MULTIDISCIPLINARY

CiteScore

1.60

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： The purpose of this journal is to catalyse, foster, and disseminate an awareness and understanding of the historical development of ideas in contemporary physics, and more generally, ideas about how Nature works. The scope explicitly includes: - Contributions addressing the history of physics and of physical ideas and concepts, the interplay of physics and mathematics as well as the natural sciences, and the history and philosophy of sciences, together with discussions of experimental ideas and designs - inasmuch as they clearly relate, and preferably add, to the understanding of modern physics. - Annotated and/or contextual translations of relevant foreign-language texts. - Careful characterisations of old and/or abandoned ideas including past mistakes and false leads, thereby helping working physicists to assess how compelling contemporary ideas may turn out to be in future, i.e. with hindsight.